Problem 83 - Prealgebra

Question

Use the definition of exponents to simplify each expression. \((2.5)^{2}\)

Step-by-Step Solution

Answer

The simplified form of \\(2.5^2\\) is 6.25.

Step 1: Understanding Exponents

The expression \((2.5)^2\) involves an exponent. The exponent indicates how many times the base, in this case, 2.5, is multiplied by itself. Here, the exponent is 2.

Step 2: Calculate the Base Raised to the Exponent

To resolve \(2.5^2\), calculate \(2.5 imes 2.5\). This equals 6.25 when performed.

Key Concepts

Understanding Base and Exponent

In mathematics, the concept of exponents is essential for expressing repeated multiplication in a simplified form. The expression \( (2.5)^2 \) involves two parts: the base and the exponent. The **base** is the number being multiplied, which in this case is 2.5. The **exponent** indicates how many times the base is multiplied by itself. Here, the exponent is 2, meaning that you need to multiply 2.5 by itself once.An exponent is written as a small number placed to the upper right of the base. It provides a concise way to show consistent multiplication, saving both space and making calculations easier to follow. For example, instead of writing 2.5 times 2.5, we use \( (2.5)^2 \) as a clean representation.

Simplifying Expressions with Exponents

Simplifying expressions with exponents involves performing the multiplication indicated by the exponent. When simplifying \( (2.5)^2 \), the exponent tells us to multiply the base by itself:

• Start by writing the multiplication: 2.5 times 2.5.
• Calculate the product, which is 6.25.

This simplification process helps transform a complex-looking expression into a simple number. The ability to quickly simplify exponent expressions is valuable in many areas of math and science, reducing errors and improving clarity in calculations. Remember, practicing simplification strengthens overall math skills by helping you understand the relationship between numbers and exponents.

Performing Mathematical Operations with Exponents

Exponents often appear in various mathematical operations, requiring you to manipulate them according to specific rules. When dealing with exponents, it's essential to apply the correct operations to arrive at the right result. Here, we focus on multiplication of the base:- Recognize when an exponent is present, as this dictates the number of multiplications.- Carefully calculate targeted multiplications, ensuring accuracy in your result.For the expression \( (2.5)^2 \):
This involves straightforward multiplication: 2.5 times 2.5, which equals 6.25. Ensuring each calculation is accurate will improve understanding and bolster confidence in working with more complex math problems. Whether in algebra or more advanced mathematics, accurate operations with exponents are fundamental to problem-solving success.